Make contraception as common and mandatory as school vaccination programs. Vasagel exists for males (and more technologies will show up down the line) and female contraception is relatively mature. Have the implants tied to RFID with expiry dates signed by manufacturers. Verifiable chain of trust. Make having babies similar to driving licenses. Whitelisting instead of trying to prevent it from occuring after the fact. The technology is there, just that everyone would hate the idea and implementation. Not to mention the societal ramifications.

What will you do when someone eventually breaks the law?